Chapter 3.5, Problem 84E

Demand for Freon 12 The demand for chlorofluorocarbon-12 (CFC-12)—the ozone-depleting refrigerant commonly known as Freon 12⁶³—has been declining significantly in response to regulation and concern about the ozone layer. The graph below represents a model for the projected demand for CFC-12 as a function of time in years.⁶⁴

Time (year since 1990)

a. Which is correct? Over the period $\left[12,20\right]$ theinstantaneous rate of change of Q is

(A) increasing. (B) decreasing.

b. Which is correct? The instantaneous rate of change of demand for Freon 12 at $t=10$

was

(A) less than (B) greater than

(C) approximately equal to the average rate of change over the interval $\left[0,20\right]$.

c. Which is correct? Over the period $\left[0,20\right]$ theinstantaneous rate of change Q is

(A) increasing, then decreasing.

(B) decreasing, then increasing.

(C) always increasing.

(D) always decreasing.

d. According to the model, the demand for Freon 12 was decreasing most rapidly around what year?

e. Roughly estimate the instantaneous rate of change of Q at $t=13$ byusing a balanced difference quotient with $h=5$. Interpret the result.